On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models

Source abstract

The basic reproduction number $R_0$ serves as a threshold parameter of many epidemic models for disease extinction or spread. The purpose of this paper is to investigate $R_0$ for spatial reaction-diffusion partial differential equation epidemic models. We define $R_0$ as the spectral radius of a product of a local basic reproduction number $R$ and strongly positive compact linear operators with spectral radii one. This definition of $R$, viewed as a multiplication operator, is motivated by the definition of basic reproduction numbers for ordinary differential equation epidemic models. We investigate the relation of $R_0$ and $R$.